Problem: Solve for $x$ and $y$ using elimination. $\begin{align*}-x-4y &= -1 \\ -7x-8y &= -5\end{align*}$
Explanation: We can eliminate $y$ when its corresponding coefficients are negative inverses. Recalling our knowledge of least common multiples, multiply the top equation by $-2$ and the bottom equation by $1$ $\begin{align*}2x+8y &= 2\\ -7x-8y &= -5\end{align*}$ Add the top and bottom equations. $-5x = -3$ Divide both sides by $-5$ and reduce as necessary. $x = \dfrac{3}{5}$ Substitute $\dfrac{3}{5}$ for $x$ in the top equation. $- \dfrac{3}{5}-4y = -1$ $-\dfrac{3}{5}-4y = -1$ $-4y = -\dfrac{2}{5}$ $y = \dfrac{1}{10}$ The solution is $\enspace x = \dfrac{3}{5}, \enspace y = \dfrac{1}{10}$.